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Related Experiment Videos

Spacetime structures of continuous-time quantum walks.

Oliver Mülken1, Alexander Blumen

  • 1Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg i.Br., Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
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Continuous-time quantum walks on lattices exhibit quantum carpet-like structures. This study relates Bloch function results to discrete quantum walks and finds longer revival times than typical quantum carpets.

Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Quantum information science

Background:

  • Continuous-time quantum walks (CTQWs) on lattices can display complex probability distributions.
  • Quantum carpets are known for their intricate patterns in quantum walk dynamics.

Purpose of the Study:

  • To investigate the structure of transition probabilities in CTQWs on 1D lattices.
  • To analyze CTQWs with periodic boundary conditions.
  • To compare CTQW dynamics with quantum carpets and discrete quantum walks.

Main Methods:

  • Calculation of transition probabilities using transfer matrix diagonalization.
  • Application of a Bloch function ansatz for periodic systems.
  • Comparison with generalized coined quantum walks.

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Main Results:

  • CTQWs on 1D lattices reveal patterns similar to quantum carpets.
  • Bloch function ansatz results are linked to discrete generalized coined quantum walks.
  • The first revival time in this CTQW system exceeds that of quantum carpets.

Conclusions:

  • The study establishes a connection between CTQWs and discrete quantum walks.
  • The observed quantum carpet-like structures and extended revival times offer new insights into quantum walk dynamics.